[/
  Copyright 2011 - 2020 John Maddock.
  Copyright 2013 - 2019 Paul A. Bristow.
  Copyright 2013 Christopher Kormanyos.

  Distributed under the Boost Software License, Version 1.0.
  (See accompanying file LICENSE_1_0.txt or copy at
  http://www.boost.org/LICENSE_1_0.txt).
]

[section:complex128 complex128]

`#include <nil/crypto3/multiprecision/complex128.hpp>`

   namespace boost{ namespace multiprecision{

   class complex128_backend;

   typedef number<complex128_backend, et_off>    complex128;

   }} // namespaces

The `complex128` number type is a very thin wrapper around GCC's `__float128` or Intel's `_Quad` data types
and provides a complex-number type that is a drop-in replacement for the native C++ floating-point types, but with
a 113 bit mantissa, and compatible with FORTRAN's 128-bit QUAD real.

All the usual standard library functions are available, performance should be equivalent
to the underlying native types.

As well as the usual conversions from arithmetic and string types, instances of `float128` are
copy constructible and assignable from GCC's `__float128` and Intel's `_Quad` data types.

Things you should know when using this type:

* Default constructed `complex128`s have the value zero.
* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware.
* It is not possible to round-trip objects of this type to and from a string and get back
exactly the same value when compiled with Intel's C++ compiler and using `_Quad` as the underlying type: this is a current limitation of
our code.  Round tripping when using `__float128` as the underlying type is possible (both for GCC and Intel).
* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted
as a valid floating-point number.
* Division by zero results in an infinity being produced.
* When using the Intel compiler, the underlying type defaults to `__float128` if it's available and `_Quad` if not.  You can override
the default by defining either `BOOST_MP_USE_FLOAT128` or `BOOST_MP_USE_QUAD`.
* When the underlying type is Intel's `_Quad` type, the code must be compiled with the compiler option `-Qoption,cpp,--extended_float_type`.

[h5 complex128 example:]

[complex128_eg]

Which results in the output:

[complex128_out]

[endsect] [/section:complex128 complex128]
